Place a large pot of heavily salted water over high heat, and bring to a boil. Add pasta to the water and boil until a bit firmer than al dente. Reserving 1 cup of pasta water, drain pasta.
Turn off the burner and set a timer for 5 minutes. Add drained pasta to the meat skillet and stir for a couple minutes.
In a mixing bowl, whisk together the eggs, yolks and grated cheese. Add some fresh pepper.
If the timer has gone off, then the pan should have cooled enough to add the sauce. The important thing is that the pan is not too hot. Pour the egg mixture onto the pasta and stir. If it looks too thick, add some of the reserved pasta water. Taste before adding salt. Serve immediately, dressing it with a bit of additional grated parmesan and pepper.